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Confidence intervals for quantiles using generalized lambda distributions

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  • Su, Steve

Abstract

Generalized lambda distributions (GLD) can be used to fit a wide range of continuous data. As such, they can be very useful in estimating confidence intervals for quantiles of continuous data. This article proposes two simple methods (Normal-GLD approximation and the analytical-maximum likelihood GLD approach) to find confidence intervals for quantiles. These methods are used on a range of unimodal and bimodal data and on simulated data from ten well-known statistical distributions (Normal, Student's T, Exponential, Gamma, Log Normal, Weibull, Uniform, Beta, F and Chi-square) with sample sizes n=10,25,50,100 for five different quantiles q=5%,25%,50%,75%,95%. In general, the analytical-maximum likelihood GLD approach works better with shorter confidence intervals and has closer coverage probability to the nominal level as long as the GLD models the data with sufficient accuracy. This technique can also be used to find confidence interval for the mode of a continuous data as well as comparing two data sets in terms of quantiles.

Suggested Citation

  • Su, Steve, 2009. "Confidence intervals for quantiles using generalized lambda distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3324-3333, July.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3324-3333
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    References listed on IDEAS

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    1. Asquith, William H., 2007. "L-moments and TL-moments of the generalized lambda distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4484-4496, May.
    2. Alan Hutson, 1999. "Calculating nonparametric confidence intervals for quantiles using fractional order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(3), pages 343-353.
    3. Su, Steve, 2007. "Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i09).
    4. Karvanen, Juha & Nuutinen, Arto, 2008. "Characterizing the generalized lambda distribution by L-moments," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1971-1983, January.
    5. Su, Steve, 2007. "Numerical maximum log likelihood estimation for generalized lambda distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3983-3998, May.
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    Cited by:

    1. Steve Su, 2016. "Flexible modelling of survival curves for censored data," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-20, December.
    2. Hund, Lauren & Schroeder, Benjamin & Rumsey, Kellin & Huerta, Gabriel, 2018. "Distinguishing between model- and data-driven inferences for high reliability statistical predictions," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 201-210.
    3. de Peretti, Christian & Siani, Carole, 2010. "Graphical methods for investigating the finite-sample properties of confidence regions," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 262-271, February.

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